Based on the numerical method proposed in [G. Hu, X. Xie, F. Xu, J. Comput. Phys., 355 (2018), 436-449.] for Kohn-Sham equation, further improvement on the efficiency is obtained in this paper by i). designing a numerical method with the strategy of separately handling the nonlinear Hartree potential and exchange-correlation potential, and ii).parallelizing the algorithm in an eigenpairwise approach. The feasibility of two approaches are analyzed in detail, and the new algorithm is described completely. Compared with previous results, a significant improvement of numerical efficiency can be observed from plenty of numerical experiments, which make the new method more suitable for the practical problems.

中文翻译：

---

关于Kohn-Sham方程的多级校正自适应有限元方法的加速

基于[G. Hu X.Xie，F.Xu，J.Comput。Phys。，355（2018），436-449。]用于Kohn-Sham方程，通过i）在本文中获得了效率的进一步提高。设计了一种数值方法，其策略是分别处理非线性Hartree势和交换相关势，并且ii）。以特征对方法并行化该算法。详细分析了两种方法的可行性，并对新算法进行了完整描述。与以前的结果相比，通过大量的数值实验可以观察到数值效率的显着提高，这使得该新方法更适合于实际问题。